Clausius-Clapeyron; just for liquids?

[ScienceNostalgia101]

In introductory chemistry at university I heard of an equation called the Clausius-Clapeyron equation relating vapour pressure to temperature of a substance. I vaguely recall hearing it applies to other liquids than just water. What I do not recall hearing is whether or not it applies solely to substances in their liquid phase. Does it apply to solids? Does it apply to solids dissolved in liquids? Does it apply to liquids dissolved in other liquids?

[studiot]

24 minutes ago, ScienceNostalgia101 said:

In introductory chemistry at university I heard of an equation called the Clausius-Clapeyron equation relating vapour pressure to temperature of a substance. I vaguely recall hearing it applies to other liquids than just water. What I do not recall hearing is whether or not it applies solely to substances in their liquid phase. Does it apply to solids? Does it apply to solids dissolved in liquids? Does it apply to liquids dissolved in other liquids?

A rather strange question considering the Clapeyron-Clausius equation (this is the right way round since Claperyon proposed it in 1837 and Clausius did not come into the picture until 1867)

is concerned to change pf phase.

 

There are two fundamental equations which govern equilibria between phases viz

1) The Phase rule (due to Gibbs) - this relates the number of components to the number of phases via the degrees of freedom

f = c - p +2  where the symbols refer to their obvious quantities.

2) The Claperyon-Clausius equation (as formally stated by Claperyon)

[math]\frac{{dP}}{{dT}} = \frac{{\Delta \bar S}}{{\Delta \bar V}} = \frac{\lambda }{{T\Delta \bar V}}[/math]

 

and applies to any change of state, (fusion, vapourisation, sublimation and changes of crystal structure)

 

Edited November 23, 2019 by studiot

[ScienceNostalgia101]

Forgot I even had this thread! Asked this for the purposes of Christmas-themed problems for my students. Realized that, tempting as a "Santa Clausius" pun would be, other  topics than Clausius-Clapeyron worked anyway.

 

That said, I'm still curious, and I'm not sure I fully understand the answer. I assume what you're saying is that if the rate of change in pressure is proportional to the rate of change in entropy with volume... therefore that entropic processes like evaporation will have to change pressure in accordance with that proportionality, making the effect of being a dissolved substance evaporating same as that of being a liquid evaporating?

 

In a nutshell, is that a "yes"?

 

Also, while I'm at it, why is it called the Clausius-Clapeyron equation if Clausius only came into the picture decades later?

[studiot]

On 1/5/2020 at 4:46 AM, ScienceNostalgia101 said:

Forgot I even had this thread! Asked this for the purposes of Christmas-themed problems for my students. Realized that, tempting as a "Santa Clausius" pun would be, other  topics than Clausius-Clapeyron worked anyway.

 

That said, I'm still curious, and I'm not sure I fully understand the answer. I assume what you're saying is that if the rate of change in pressure is proportional to the rate of change in entropy with volume... therefore that entropic processes like evaporation will have to change pressure in accordance with that proportionality, making the effect of being a dissolved substance evaporating same as that of being a liquid evaporating?

 

In a nutshell, is that a "yes"?

 

Also, while I'm at it, why is it called the Clausius-Clapeyron equation if Clausius only came into the picture decades later?

OK there are different versions of the equations and different subsequent authors apply different names.

The original equations were developed for liquid- gas phase transitions, but modern trends are to generalise as far as possible and this is the version I quoted.

Here is a somewhat older description, sticking to the liquid- gas model and showing how the versions are appled practically.

Starting with equation 21 this is the original Clapeyron statement.

Equations 24 and 27 were developed by Clausius from this.